I think the only home brew thing I would try is very mild hand soap and warm water. Maybe a drop or two in half cup or so of water. no abrasive cloths! Something cotton should be OK.
I had some movers move my test lab at Lexmark. They put all the moving labels on the screen and removed them with alky... not a good thing to do. 32 LCD monitors were turned into junk.
I think the worst I've seen lately is this one place I go into where some of the employees dip. Of course they cough and crap all over the screen and scrape if off with their fingers. Nice way to destroy a screen.